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Homework Help: Cartesian vector application involving two forces.

  1. Jun 27, 2008 #1
    1. The problem statement, all variables and given/known data

    Two forces act on an object at an angle of 50°. One force is 150 N. The resultant
    force is 200 N. Find the second force and the angle that it makes with the
    resultant.


    2. Relevant equations

    Ux=|U|cos(theta)
    Uy=|U|sin(theta)

    3. The attempt at a solution

    Basically I began by trying to find the components of the 150 N force by using the formulas mentioned above, which left me with U = [150, 0]. I then tried adding the two forces together, i.e. R = [150 + vx, 0 + vy] and then tried to find the magnitude of the resultant, which I knew was equal to 200. I squared both sides leaving me with (150 + vx)^2 + (0 + vy)^2 = 40000, however I did not know where to go from here. Any help is appreciated, thanks alot.
     
  2. jcsd
  3. Jun 27, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You haven't made use of the 50° angle. Assume that second force has a magnitude of F and makes an angle of 50° with respect to the x-axis. Use its components in the equation you wrote.
     
  4. Jun 27, 2008 #3
    If I'm understanding this correctly, could I assume that Vx=0.6428F and Vy=0.7660F and use those directly in my (150 + vx)^2 + (0 + vy)^2 = 40000 equation or would I have to use Fcos(50) and Fsin(50) instead? Thanks for the help so far.
     
  5. Jun 27, 2008 #4

    Doc Al

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    Staff: Mentor

    Either way will work, as sin(50) = 0.7660 (at least to a good approximation). Personally, I would use cos(50) and sin(50), only plugging in values in the last step.
     
  6. Jun 27, 2008 #5
    Will do, Thanks alot Doc Al.
     
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